提出面向三角网格法向量的新型二阶变分模型，提升去噪效果。
Total Generalized Variation of the Normal Vector Field and Applications to Mesh Denoising
- 将法向量视为球面上的流形值函数，构建切向Raviart-Thomas有限元空间
- 在网格去噪实验中优于现有方法，有效保留几何细节
- 适合需要高保真几何处理的三维重建与逆向工程场景
我们提出了一种在嵌入于ℝ³的定向三角网格上，对法向量场进行二阶总广义变分（TGV）的新公式。法向量被视作取值于单位球面的流形值函数。该公式扩展了先前针对分片常数标量数据的离散TGV模型，这些模型使用Raviart-Thomas函数空间。为将其推广至流形设置，本文构建了一个定制化的切向Raviart-Thomas型有限元空间。新正则化项在网格去噪实验中与现有方法进行了对比。
原文摘要 · Abstract (English)
We propose a novel formulation for the second-order total generalized variation (TGV) of the normal vector on an oriented, triangular mesh embedded in $\R^3$. The normal vector is considered as a manifold-valued function, taking values on the unit sphere. Our formulation extends previous discrete TGV models for piecewise constant scalar data that utilize a Raviart-Thomas function space. To extend this formulation to the manifold setting, a tailor-made tangential Raviart-Thomas type finite element space is constructed in this work. The new regularizer is compared to existing methods in mesh denoising experiments.
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